View source for Air Classifier (Altun)

== Description ==

This article describes the '''Altun and Benzer''' (2014) model for air classification.{{Altun and Benzer (2014)}}

== Model theory ==

{{Under construction|section}}

== Excel ==

The Altun air classifier model may be invoked from the Excel formula bar with the following function call:

<syntaxhighlight lang="vb">=mdUnit_AirClassifier_Altun(Parameters as Range, Size as Range, Feed as Range, OreSG Range)</syntaxhighlight>

{{Excel (Text, Help, No Arguments)}}

=== Inputs ===

{{Excel (Text, Inputs)}}

:<math>Parameters=
\begin{bmatrix}
D\text{ (m)}\\
{\rm AF}\text{ (m}^3\text{/h)}\\
{\rm RS}\text{ (m/s)}\\
k_{\alpha}\\
n_{\alpha}\\
k_{d_{50}}\\
n_{d_{50}}\\
k_{C}\\
n_{C}\\
k_{\beta}\\
n_{\beta}\\
c_{\beta}\\
(Q_{\rm M,F})_{\rm L}\text{ (t/h)}\\
\end{bmatrix},\;\;\;\;\;\;

Size = \begin{bmatrix}
d_{1}\text{ (mm)}\\ 
\vdots\\ 
d_p\text{ (mm)}\\ 
\end{bmatrix},\;\;\;\;\;\;

Feed= \begin{bmatrix}
(Q_{\rm M,F})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{1m}\text{ (t/h)}\\ 
\vdots & \ddots & \vdots\\ 
(Q_{\rm M,F})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{nm}\text{ (t/h)}\\ 
\end{bmatrix},\;\;\;\;\;\;

OreSG= \begin{bmatrix}
(\rho_{\rm S})_{1}\text{ (t/m}^\text{3}\text{)} & \dots & (\rho_{\rm S})_m\text{ (t/m}^\text{3}\text{)}\\ 
\end{bmatrix}

</math>

where:
* <math>D</math> is the classifier chamber diameter (m)
* <math>{\rm AF}</math> is the air flow rate  (m<sup>3</sup>/h)
* <math>{\rm RS}</math> is rotor speed (m/s)
* <math>k</math> is an equation coefficient
* <math>n</math> is an equation exponent
* <math>c</math> is an equation constant
* <math>(Q_{\rm M,F})_{\rm L}</math> is the mass flow rate of liquids in the feed (t/h)'
* <math>p</math> is the number of size intervals
* <math>m</math> is the number of ore types
* <math>d_i</math> is the size of the square mesh interval that mass is retained on (mm)
* <math>d_{i+1}<d_i<d_{i-1}</math>, i.e. descending size order from top size (<math>d_{1}</math>) to sub mesh (<math>d_{p}=0</math> mm)
* <math>\rho_{\rm S}</math> is the density of solids (t/m<sup>3</sup>)

=== Results ===

The results are displayed in Excel as an array corresponding to the matrix notation below:

:<math>
\mathit{mdUnit\_AirClassifier\_Altun} = 
\begin{bmatrix}

\begin{bmatrix}
{\rm DL}\text{ (kg/m}^3\text{)}\\
F\text{ (t/h)}\\
\alpha\\
d_{\rm 50c}\text{ (mm)}\\
C\text{ (frac)}\\
\beta\\
\beta^*\\
(Q_{\rm M,OF})_{\rm L}\text{ (t/h)}\\
(Q_{\rm M,UF})_{\rm L}\text{ (t/h)}\\
\end{bmatrix}


\begin{array}{cccccc}

\begin{bmatrix}
\bar d_1\text{ (mm)}\\
\vdots\\
\bar d_n\text{ (mm)}
\end{bmatrix}


&

\begin{bmatrix}
(Q_{\rm M,UF})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,UF})_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
(Q_{\rm M,UF})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,UF})_{nm}\text{ (t/h)}\\
\end{bmatrix}

&

\begin{bmatrix}
(Q_{\rm M,OF})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,OF})_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
(Q_{\rm M,OF})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,OF})_{nm}\text{ (t/h)}\\
\end{bmatrix}

&

\begin{bmatrix}
(P_{\rm OF})_1\text{ (frac)}\\
\vdots\\
(P_{\rm OF})_n\text{ (frac)}
\end{bmatrix}
\\
\\
\\
\\
\\
\\
\\
\end{array}

\end{bmatrix}
</math>


where:
* <math>{\rm DL}</math> is the dust loading (kg/m<sup>3</sup>)
* <math>F</math> is the flow rate of -36+3 µm size particles in the feed (t/h)
* <math>\alpha</math> is the sharpness parameter of the [[Partition (Size, Whiten-Beta)|Whiten-Beta]] efficiency curve
* <math>d_{\rm 50c}</math> is the cut size parameter of the [[Partition (Size, Whiten-Beta)|Whiten-Beta]] efficiency curve (mm)
* <math>C</math> is the bypass parameter of the [[Partition (Size, Whiten-Beta)|Whiten-Beta]] efficiency curve (frac)
* <math>\beta</math> is a fish-hook parameter of the [[Partition (Size, Whiten-Beta)|Whiten-Beta]] efficiency curve
* <math>\beta^*</math> is a fish-hook parameter of the [[Partition (Size, Whiten-Beta)|Whiten-Beta]] efficiency curve
* <math>(Q_{\rm M,OF})_{\rm L}</math> is the mass flow rate of liquids to the overflow stream (t/h)
* <math>(Q_{\rm M,UF})_{\rm L}</math> is the mass flow rate of liquids to the underflow stream (t/h)
* <math>P_{\rm OF}</math> is the partition fraction to overflow (frac)

=== Example ===

The images below show the selection of input arrays and output results in the Excel interface.

{|
|- style="vertical-align:top;"
| [[File:AirClassifierAltun1.png|left|frame|Figure 1. Example showing the selection of the '''Parameters''' (blue frame) array in Excel.]]
| [[File:AirClassifierAltun2.png|left|frame|Figure 2. Example showing the selection of the '''Size''' (red frame), '''OreSG''' (green frame) and '''Feed''' (purple frame) arrays in Excel.]] 
| [[File:AirClassifierAltun3.png|left|frame|Figure 3. Example showing the selection of the '''Results''' (light blue frame) array in Excel.]]
|}

== SysCAD ==

{{Under construction|section}}

== References ==

[[Category:Excel]]
[[Category:SysCAD]]